Introduction to real orthogonal polynomials
By: by William H. Thomas, II
Contributors: Fischer, Ismor
Publisher: Naval Postgraduate School; Available from the National Technical Information Service
Published: 1992
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Number of pages: 105
Description: The fundamental concept of orthogonality of mathematical objects occurs in a wide variety of physical and engineering disciplines. The theory of orthogonal functions, for example, is central to the development of Fourier series and wavelets, essential for signal processing. In particular, various families of classical orthogonal polynomials have traditionally been applied to fields such as electrostatics, numerical analysis, and many others. This thesis develops the main ideas necessary for understanding the classical theory of orthogonal polynomials. Special emphasis is given to the Jacobi polynomials and to certain important subclasses and generalizations, some recently discovered. Using the theory of hypergeometric power series and their q -extensions, various structural properties and relations between these classes are systematically investigated. Recently, these classes have found significant applications in coding theory and the study of angular momentum, and hold much promise for future applications. orthogonal polynomials, hypergeometric series.
Notes: Thesis advisor, Ismor Fischer.

Thesis (M.S. in Applied Mathematics) Naval Postgradaute School, June 1992.

Includes bibliographical references.

Also available online.

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